Smooth and sparse hyperspectral unmixing using an l0 penalty

Hyperspectral unmixing is an important technique for analyzing hyperspectral remote sensing images. We propose an estimation algorithm that, simultaneously, encourages smoothness in the endmembers and sparseness in the abundances by using first order roughness and l0 penalties. The method is evaluated both on simulated data and a real hyperspectral image of an urban landscape.

[1]  John F. Mustard,et al.  Spectral unmixing , 2002, IEEE Signal Process. Mag..

[2]  Sen Jia,et al.  Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[3]  B. Silverman,et al.  Nonparametric regression and generalized linear models , 1994 .

[4]  D. Hunter,et al.  A Tutorial on MM Algorithms , 2004 .

[5]  Victor Solo A sure-fired way to choose smoothing parameters in ill-conditioned inverse problems , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[6]  José M. Bioucas-Dias,et al.  Vertex component analysis: a fast algorithm to unmix hyperspectral data , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[7]  Patrik O. Hoyer,et al.  Non-negative sparse coding , 2002, Proceedings of the 12th IEEE Workshop on Neural Networks for Signal Processing.

[8]  Daniel D. Lee,et al.  Multiplicative Updates for Nonnegative Quadratic Programming in Support Vector Machines , 2002, NIPS.

[9]  Jun Zhou,et al.  Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[10]  Jérôme Idier,et al.  Algorithms for Nonnegative Matrix Factorization with the β-Divergence , 2010, Neural Computation.

[11]  Antonio J. Plaza,et al.  Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[12]  Alan R. Gillespie,et al.  Autonomous atmospheric compensation (AAC) of high resolution hyperspectral thermal infrared remote-sensing imagery , 2000, IEEE Trans. Geosci. Remote. Sens..

[13]  B. Silverman,et al.  Nonparametric Regression and Generalized Linear Models: A roughness penalty approach , 1993 .

[14]  D. Cox Nonparametric Regression and Generalized Linear Models: A roughness penalty approach , 1993 .

[15]  Johannes R. Sveinsson,et al.  A smooth hyperspectral unmixing method using cyclic descent , 2012, 2012 IEEE International Geoscience and Remote Sensing Symposium.

[16]  C. Stein Estimation of the Mean of a Multivariate Normal Distribution , 1981 .

[17]  Thierry Blu,et al.  Monte-Carlo Sure: A Black-Box Optimization of Regularization Parameters for General Denoising Algorithms , 2008, IEEE Transactions on Image Processing.

[18]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .